Why would leaders hold soldiers around the workplace after the day's work is complete and there is nothing else to be done?

You're a sergeant. You are the guy who should know the answer, and if you don't then ask the next NCO in you chain until you find the answer.

My guess is that there is some reason for keeping the soldiers readily available. It may not be apparent to the people doing the sitting, but there's a senior NCO or Officer who knows the reason. That's not to say it's a good reason. You may get something like, "three months ago, we let everybody off duty at 1500 because all the work was done. At 1625 the Installation Commander dropped by and the only person in the building was the CO. The CO was embarrassed, so he decided we would have personnel available for duty until the official close of duty time." An even worse, but equally probable answer, "in the 69th Brigade, we've always done it this way." Don't doubt that stuff like this happens.

Since I went from Active Duty into the Reserves, I can provide my view point from a few different units I've been a part of. In my Reserves unit, we do often have to hang around a bit while the senior NCOs and leadership have a few final meetings to make sure everything is done and all the information is put out. It is up to us to be gainfully employed while this occurs but even we'll be waiting around to be dismissed.

When I was a junior enlisted, my NCOs would try to look after us. They would release a few of us if nothing was going on and rotate who was let go early while a couple of us stayed behind doing the usual daily tidying up, or last minute missions that crop up. I had NCOs that went to our OICs to see if we could be released.

When I redeployed, our unit had a lot of soldiers who sat around and had no mission while we were waiting to be released from our unit to go to our next unit, which took several months. Many times, the orders were handed down as to be somewhere else but keep our phones on in case of a recall formation, because an S6 with 30 soldiers sitting around and 4 computers to use looked worse than a skeleton crew, and us using the library or training center computers for some gainful use of time (SSDs, etc).

When I became one of the lead NCOs at my last active duty unit, we were almost always release by section except Fridays when we needed to check with 1SG (for safety brief). So as long as my OIC didn't need the soldiers, I'd check with him/her and release all but whoever I needed. They understood that there would be other times I'd need them to work late, so letting them go early was my "don't complain when I ask you to stay late" pass. There were times we had training that needed to be accomplished as well, but it is a good NCO that will know what the training schedule has on it, and spread it out across the soldiers' time so they aren't bored or over worked. They knew if I let them all go and the trash wasn't taken out, or the floors swept, that it'd be the NCOs finishing up the work so they knew to pitch in before going. It makes for a better working relationship with the troops when they know the NCO is trying to take care of them and not waste their time. There have been times when 1SG wants bodies sent over to HQ for area beautification and my platoon sergeant (E7) and I would go instead of sending the junior enlisted because we had them actively engaged in things meant to better their career or improve their job performance and we didn't want that interrupted.

I learned from good NCOs to take care of my soldiers because they took care of me. If you see a problem, work with other NCOs towards solutions.

Had that happen in one of my reserve units all of the time. We would always get told in morning formation that we had a lot on the training schedule and it was up to us what time we got to get out. No matter how many times we completed all tasks to standard and got everything cleaned up, inevitably we'd be sitting around doing nothing waiting on senior leadership to allow us to go. There were multiple times we'd be sitting there and it would be past the time to go, according to the training schedule, just waiting to have final formation. I remember once, we didn't get out because the CO was meeting with an E-6, who was transitioning to be an officer in the Coast Guard. Meeting started after we were supposed to leave (mind you with all tasks completed), and we had to wait for that 90-minute long meeting to get over, just so we could do a goodbye to the E-6 and have cake.